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Mechanics of Composite Elasmoid Fish Scale Assemblies and Their journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 Available online at www.sciencedirect.com www.elsevier.com/locate/jmbbm Mechanics of composite elasmoid fish scale assemblies and their bioinspired analogues Ashley Browninga, Christine Ortizb,n, Mary C. Boycea,n aDepartment of Mechanical Engineering, 77 Massachusetts Ave, Massachusetts Institute of Technology, Cambridge, MA, USA bDepartment of Materials Science and Engineering, 77 Massachusetts Ave, Massachusetts Institute of Technology, Cambridge, MA, USA article info abstract Article history: Inspired by the overlapping scales found on teleost fish, a new composite architecture Received 28 July 2012 explores the mechanics of materials to accommodate both flexibility and protection. These Received in revised form biological structures consist of overlapping mineralized plates embedded in a compliant 5 November 2012 tissue to form a natural flexible armor which protects underlying soft tissue and vital Accepted 11 November 2012 organs. Here, the functional performance of such armors is investigated, in which the Available online 24 November 2012 composition, spatial arrangement, and morphometry of the scales provide locally tailored Keywords: functionality. Fabricated macroscale prototypes and finite element based micromechanical Biomimetic models are employed to measure mechanical response to blunt and penetrating indentation Composite loading. Deformation mechanisms of scale bending, scale rotation, tissue shear, and tissue Natural armor constraint were found to govern the ability of the composite to protect the underlying Fish scale substrate. These deformation mechanisms, the resistance to deformation, and the resulting work of deformation can all be tailored by structural parameters including architectural arrangement (angle of the scales, degree of scale overlap), composition (volume fraction of the scales), morphometry (aspect ratio of the scales), and material properties (tissue modulus and scale modulus). In addition, this network of armor serves to distribute the load of a predatory attack over a large area to mitigate stress concentrations. Mechanical characterization of such layered, segmented structures is fundamental to developing design principles for engineered protective systems and composites. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction et al., 2012; Gemballa and Bartsch, 2002; Ibanez et al., 2009; Jawad and Al-Jufaili, 2007; Sire et al., 2009; Vernerey and Fish scale assemblies provide a diversity of natural engi- Barthelat, 2010). This study focuses on ‘‘elasmoid’’ scale assem- neered designs which achieve multiple functionalities including blies of teleost fish. Individual elasmoid scales are composed of mechanical protection, anisotropic flexibility, hydration, regen- a mineralized outer layer (16–59 vol%) of hydroxyapatite eration, repair, and camouflage (Arciszewski and Cornell, 2006; (Garrano et al., 2012; Torres et al., 2008; Whitear, 1986; Zhu Colbert and Morales, 2001). Examples of design categories of et al., 2012) whose geometry is an ellipsoidal or rectangular fish scale assemblies include structure and composition of the plate with aspect ratios of 25–100. Elasmoid scales are imbri- individual scale (layering), morphometrics or shape of indivi- cated (overlapping), non-articulating and embedded within a dual scales, composite design, inter-scale connections and compliant non-mineralized tissue (Fig. 1), with varying scale joints, and scale assembly spatial arrangements (Garrano aspect ratio, scale orientation angle, spatial overlap, and volume nCorresponding authors. E-mail addresses: [email protected] (C. Ortiz), [email protected] (M.C. Boyce). 1751-6161/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmbbm.2012.11.003 76 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 Fig. 1 – Overview of the structure of elasmoid fish scale assemblies. (a) Integument of a fresh Atlantic salmon (Salmo salar) obtained from a local fishery (New Deal Fish Market, Cambridge, MA). Image adapted from O¨ stman, Elisabeth, Iduns kokbok, 1911, Web, Last accessed on May 1, 2012. http://commons.wikimedia.org/wiki/Salmo_salar, (b) overlapping scales and underlying tissue were excised from the main body and caudal peduncle (tail) near the lateral line and (c) micro-computed tomography (lCT) was employed to obtain two-dimensional slices (false coloring) of structure. Scans were performed and analyzed following our previously reported methods (Connors et al., 2012; Song et al., 2010). Scales are embedded in a dermal tissue at various geometric configurations, which are summarized (d). fraction of scales, creating a robust composite system in which where digital image correlation (DIC) was used to measure the interplay between the mineralized scales and the compliant the strain fields in the composite material. These experimental tissue plays a governing role in tailoring and controlling and numerical models yield detailed insights into the roles and mechanical behavior and deformation mechanisms. This com- the tradeoffs of the composite structure providing constraint, posite structure varies not only across species, but also along shear, and bending mechanisms to impart protection and the body of individual fish as found by histological sections flexibility. (Hawkes, 1974; Park and Lee, 1988; Sire, 1990; United States Fish and Wildlife Service, 2010; Whitear, 1986). Experimental measurements of mechanical properties of elasmoid scales have been limited to the macroscale 2. Materials and methods mechanics of an individual scale resisting penetration by a sharp indenter or uniaxial tensile testing. Testing of scales in 2.1. Geometry of elasmoid fish scale assembly a hydrated state found the tensile strength to range between 22 and 65 MPa and the toughness to be 1 MPa (Garrano The primary features of the structure of mineralized scales et al., 2012; Ikoma et al., 2003; Meyers et al., 2012; Torres et al., embedded in a soft tissue are captured in a micromechanical 2008; Zhu et al., 2012). The multilayered elasmoid fish scale model consisting of (1) an upper layer of relatively high was found to localize penetration by promoting cross-like modulus (Es) scale of aspect ratio Ls=ts oriented at angle y fracture patterns in the outer layer (Zhu et al., 2012). On a and embedded in a low modulus (Et) tissue, and (2) a soft (low larger length scale, Vernerey and Barthelat (2010) introduced modulus Et) tissue substrate support (representing the under- a two-dimensional mathematical model of overlapping fish lying collagenous layer) as shown in Fig. 1(c,d). scales where accommodation of bending is determined as a Typical values for the scale thickness in teleost fish are on function of scale geometry and material properties. They the order of ts0:1 mm, but reported values range from found that a strain-stiffening behavior of the assembly with 44 mmto1mm,(Whitenack et al., 2010; Meyers et al., 2012). increasing scale overlap provides the ability to distribute Typical scale lengths, Ls, range from 5 to 15 mm, but have deformation over a large area during bending. been reported over 100 mm long (Francis, 1990; Garrano et al., In this paper, a three-dimensional elastic, composite model 2012; Jawad and Al-Jufaili, 2007; Meyers et al., 2012; Torres was formulated for the case of the mineralized scales fully et al., 2008; Zhu et al., 2012). Despite the large range of embedded in a compliant hyperelastic organic tissue matrix. observed scale lengths and thicknesses, the geometry of the Loading under the physiologically relevant conditions of fish scale preserves an aspect ratio Ra ¼ Ls=ts between 25 and blunt trauma and indentation is simulated as a function of 100 based on the available literature and measurements. The scale material properties, aspect ratio, scale orientation effect of various geometric parameters will be studied (as angle, spatial overlap, and volume fraction of scales. The discussed later) but the scale will be held at constant aspect simulations allow for identification of deformation mechan- ratio of either Ra ¼50 or 100, which were taken as intermedi- isms, including the roles of scale bending, tissue shear, and ate and maximum values, respectively. scale rotation as a function of scale geometry, and the The scales are initially oriented at angle y relative to a quantification of back-deflection, work of deformation, and compliant tissue support (Fig. 1d). Scales overlap each other spatially heterogeneous stress fields. Macroscale synthetic such that a fraction of the scale is embedded beneath an models were constructed from an engineering thermoplastic adjacent scale. The length d is the exposed length of scale, and silicone rubber using a combination of three-dimensional while the remaining length (LsÀd) is embedded beneath printing and molding fabrication methods. The synthetic mod- another scale. This degree of imbrication, or overlap, els were experimentally tested to measure the mechanical Kd ¼ d=Ls is a measure for the spatial overlap defined by performance and to validate the model predictions. Mechanical Burdak (1979), who measured Kd for 16 species of the behavior under blunt compressive loading was measured Cyprinidae family of fish and found that values range from journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 77 0:24rKdr1 depending on species and body location. Fish 1 with highly overlapping, heavily armored skins such as the 40 tench (Tinca tinca),
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